From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4574 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Sat, 13 Sep 2008 13:17:23 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020036 13906 80.91.229.2 (29 Apr 2009 15:47:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:16 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Sat Sep 13 19:16:52 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 13 Sep 2008 19:16:52 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KedKh-0005rt-1I for categories-list@mta.ca; Sat, 13 Sep 2008 19:11:11 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 44 Original-Lines: 91 Xref: news.gmane.org gmane.science.mathematics.categories:4574 Archived-At: Dear Colin, Zoran, Robert, Eduardo and All, I find the present discussion on Bourbaki and category theory very = important. =20 I recall asking the question to Samuel Eilenberg 25 years ago and more = recently to Pierre Cartier. =20 If my recollection is right, Bourbaki had essentially two options: = rewrite the whole treaty using categories,=20 or just introduce them in the book on homological algebra,=20 The second option won, essentially because of the enormity of the task = of rewriting everything.=20 Other factors may have contributed on a smaller scale, like some = unresolved foundational questions.=20 In any cases, it was the beginning of end for Bourbaki. Bourbaki was a great humanistic and scientific enterprise. Advanced mathematics was made available to a large number of students, possibly over the head of their bad teachers.=20 It defended the unity and rationality of science in an age of growing irrationalism (it was conceived in the mid thirties). I have personally learned a lot of mathematics by reading Bourbaki. =20 Everything was proved, and the proofs were logically very clear. It was a like a continuation of Euclid Elements two thousand years = later! But after a while, I stopped reading it. I had realised that something important was missing: the motivation.=20 The historical notes were very sketchy and not integrated to the text. I remember my feeling of frustration in reading the books of functional = analysis, because the applications to partial differential equations were not = described. Everything was presented in a deductive order, from top to down. We all know that learning is very much an inductive process, from the particular to the general. This is true also of mathematical = research.=20 Bourbaki is dead but I hope that the humanistic philosophy behind the = enterprise is not. =20 Unfortunately, we presently live in an era of growing irrationalism. Science still needs to be defended against religion. Civilisation maybe at a turning point with the problem of climate = change.=20 Millions of people need and want to learn science and mathematics.=20 Should we not try to give Bourbaki a second life?=20 It will have to be different this time. Possibly with a new name. Obviously, internet is the medium of choice. What do you think? Andre -------- Message d'origine-------- De: cat-dist@mta.ca de la part de Colin McLarty Date: ven. 12/09/2008 14:46 =C0: categories@mta.ca Objet : categories: Re: Bourbaki and Categories =20 From: zoran skoda Date: Friday, September 12, 2008 2:06 pm wrote, among other things > main points of departure. The remark that as a proponent of=20 > "structures" Bourbaki > had to include categories is anyway a bit lacking an argument.=20 > First of all, because > of the size problems one can not take big categories on equal=20 > footing with, say groups, > and considering only small categories would be strange and lacking=20 > most interesting examples. The claim is not that Bourbaki should have studied categories as structures. It is that Bourbaki was doomed to fail in trying to use their structure theory. Leo Corry shows in his book "Modern Algebra and the Rise of Mathematical Structures" (Birkh=E4user 1996) that they did = fail. =20 And they should have seen this coming, because their theory had been=20 "superseded by that of category and functor, which includes it under a more general and convenient form" (Dieudonn=E9 "The Work of Nicholas Bourbaki" 1970). best, Colin